mlsanityData to 7 Oct 2026

Error-driven Input Modulation: Solving the Credit Assignment Problem without a Backward Pass

arXiv 2201.11665 ↗First posted 27 Jan 2022cs.NEcited by 63

Not on the map. Why?

Abstract (arXiv)

Supervised learning in artificial neural networks typically relies on backpropagation, where the weights are updated based on the error-function gradients and sequentially propagated from the output layer to the input layer. Although this approach has proven effective in a wide domain of applications, it lacks biological plausibility in many regards, including the weight symmetry problem, the dependence of learning on non-local signals, the freezing of neural activity during error propagation, and the update locking problem. Alternative training schemes have been introduced, including sign symmetry, feedback alignment, and direct feedback alignment, but they invariably rely on a backward pass that hinders the possibility of solving all the issues simultaneously. Here, we propose to replace the backward pass with a second forward pass in which the input signal is modulated based on the error of the network. We show that this novel learning rule comprehensively addresses all the above-mentioned issues and can be applied to both fully connected and convolutional models. We test this learning rule on MNIST, CIFAR-10, and CIFAR-100. These results help incorporate biological principles into machine learning.

Key facts. Cited by 63 papers in the map (data through 7 Oct 2026). First posted on arXiv 27 Jan 2022.

Builds on

No reference list yet.

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 1; 2023: 13; 2024: 21; 2025: 17; 2026: 11.

63 papers.

Sort:

  1. 2023The Predictive Forward-Forward Algorithmcited by 35
  2. 2023Brain-inspired Computational Intelligence via Predictive Codingcited by 30
  3. 2023Forward Learning with Top-Down Feedback: Empirical and Analytical Characterizationcited by 13
  4. 2023Training Convolutional Neural Networks with the Forward-Forward algorithmcited by 13
  5. 2024Training Machine Learning models at the Edge: A Surveycited by 11
  6. 2023The Trifecta: Three simple techniques for training deeper Forward-Forward networkscited by 10
  7. 2024Momentum Auxiliary Network for Supervised Local Learningcited by 9
  8. 2023Graph Neural Networks Go Forward-Forwardcited by 8
  9. 2023Improving equilibrium propagation without weight symmetry through Jacobian homeostasiscited by 8
  10. 2024FFCL: Forward-Forward Net with Cortical Loops, Training and Inference on Edge Without Backpropagationcited by 6
  11. 2024Advancing Supervised Local Learning Beyond Classification with Long-term Feature Bankcited by 6
  12. 2024Beyond Backpropagation: Optimization with Multi-Tangent Forward Gradientscited by 6
38 more
  1. 2023Extending the Forward Forward Algorithmcited by 5
  2. 2024On-device Online Learning and Semantic Management of TinyML Systemscited by 5
  3. 2024LLS: Local Learning Rule for Deep Neural Networks Inspired by Neural Activity Synchronizationcited by 5
  4. 2024MLAAN: Scaling Supervised Local Learning with Multilaminar Leap Augmented Auxiliary Networkcited by 5
  5. 2024HPFF: Hierarchical Locally Supervised Learning with Patch Feature Fusioncited by 5
  6. 2024Counter-Current Learning: A Biologically Plausible Dual Network Approach for Deep Learningcited by 5
  7. 2024Poor Man's Training on MCUs: A Memory-Efficient Quantized Back-Propagation-Free Approachcited by 5
  8. 2025Backpropagation-free Spiking Neural Networks with the Forward-Forward Algorithmcited by 5
  9. 2024Towards Interpretable Deep Local Learning with Successive Gradient Reconciliationcited by 4
  10. 2025TESS: A Scalable Temporally and Spatially Local Learning Rule for Spiking Neural Networkscited by 4
  11. 2023Feed-Forward Optimization With Delayed Feedback for Neural Network Trainingcited by 3
  12. 2024LightFF: Lightweight Inference for Forward-Forward Algorithmcited by 3
  13. 2024Towards training digitally-tied analog blocks via hybrid gradient computationcited by 3
  14. 2024Temporal-Difference Learning Using Distributed Error Signalscited by 3
  15. 2025Mono-Forward: Revisiting Forward-Forward through Objective-Locality Decompositioncited by 3
  16. 2025MAN++: Scaling Momentum Auxiliary Network for Supervised Local Learning in Vision Taskscited by 3
  17. 2023Polarity is all you need to learn and transfer fastercited by 2
  18. 2023Node Perturbation Can Effectively Train Multi-Layer Neural Networkscited by 2
  19. 2024DFA-GNN: Forward Learning of Graph Neural Networks by Direct Feedback Alignmentcited by 2
  20. 2025Closed-Form Feedback-Free Learning with Forward Projectioncited by 2
  21. 2025LANCE: Low Rank Activation Compression for Efficient On-Device Continual Learningcited by 2
  22. 2026Covariance-Aware Goodness for Scalable Forward-Forward Learningcited by 2
  23. 2023Understanding Predictive Coding as an Adaptive Trust-Region Methodcited by 1
  24. 2023Intrinsic Biologically Plausible Adversarial Robustnesscited by 1
  25. 2024Learning Using a Single Forward Passcited by 1
  26. 2024Forward Learning of Graph Neural Networkscited by 1
  27. 2024On the Improvement of Generalization and Stability of Forward-Only Learning via Neural Polarizationcited by 1
  28. 2024Replacement Learning: Training Vision Tasks with Fewer Learnable Parameterscited by 1
  29. 2025Stochastic Layer-wise Learning: Scalable and Efficient Alternative to Backpropagationcited by 1
  30. 2025Adaptive Spatial Goodness Encoding: Advancing and Scaling Forward-Forward Learning Without Backpropagationcited by 1
  31. 2025Traces Propagation: Memory-Efficient and Scalable Forward-Only Learning in Spiking Neural Networkscited by 1
  32. 2025Feedback Alignment Meets Low-Rank Manifolds: A Structured Recipe for Local Learningcited by 1
  33. 2025NetworkFF: Unified Layer Optimization in Forward-Only Neural Networkscited by 1
  34. 2026HCL-FF: Hierarchical and Contrastive Learning for Forward-Forward Algorithmcited by 1
  35. 2026Conditioned Direct Feedback Alignment via Activity and Error Geometrycited by 1
  36. 2022Biologically Plausible Training of Deep Neural Networks Using a Top-down Credit Assignment Networkcited by 0
  37. 2024Training Large-Scale Optical Neural Networks with Two-Pass Forward Propagationcited by 0
  38. 2025Forward Target Propagation: A Forward-Only Approach to Global Error Credit Assignment via Local Lossescited by 0

50 most cited of 63 All 63 (JSON)